this metric is kind of poor. What about something like the area ratio of the biggest inscribed rectangle to the smallest circumscribed rectangle that has edges parallel to the selected inscribed rectangle.
I like this metric better, although I'm wondering if the rectangles should be similar, not just having parallel edges. That should put Turkey and Portugal up at the top, if you remove the islands.
It seems like it would be an excellent method if you could address the outlier issue though. One approach would be to relax the rectangles, so the outer one only has to circumscribe 95% of the country's area.
A similar approach is used in biology to define animal territories: A kernel density estimate is taken of historical animal positions and thresholded, rather than a minimum convex polygon.